Based on our previous result, the statement can be traced back to existing results in
the literature. Since \(z^*\)  is a KKT point of REF , we know
that the bi-active set \( \lbrace  i \ | \ x_i^* = 0 = y_i^* \rbrace  \)  is empty. Therefore, it
follows from assumption \( (i) \)  and Theorem REF 
that ordinary LICQ holds for REF  at \(z^*\) . Similarly, assumption \( (ii) \) 
and Theorem REF  imply that the strong second-order sufficiency conditions holds
for REF  at \(z^*\) . Standard results on the local convergence of nonsmooth
Newton methods then imply that all elements \( H \in \partial _B T (z^*) \)  are
nonsingular, see, e.g., [1]}, [2]}, [3]}.
